One less restrictive constraint is the requirement that the temperature PDF be nonnegative. This constraint applies the physical law that there cannot be fewer than zero molecules at any temperature. Because a least-squares solution via SVD will fit oscillating functions to the \(PDF(T)\)  curve, a solution without the non-negative constraint will contain temperatures with negative \(H_2O\)  density as in Figure REF a, particularly around the discontinuity at \(T_{max}\) . By applying the non-negative constraint, an algorithm must find the most similar solution which cuts out the negative oscillations of the TSVD. Algorithms which use the non-negative constraint, like MATLAB’s \(lsqnonneg\)  function [1]}, tend to produce a discontinuous PDF as in Figure REF b which is no more realistic than the TSVD solution.
